
Here, \( \lambda \)  is the carrier wavelength, \( \beta _{1} \)  is the path-loss between the BS and the IRS. Also, \( d_{\mathrm {BS}} \)  and \( d_{\mathrm {IRS}} \)  are the inter-antenna separation at the BS and inter-element separation at the IRS, respectively [1]}. The elevation and azimuth LoS angles of departure (AoD) at the BS with respect to IRS element \( n \)  are described by \( \theta _{1,n} \)  and \( \varphi _{1,n} \) . The elevation and azimuth LoS angles of arrival (AoA) at the IRS are described by \( \theta _{2,n} \)  and \( \varphi _{2,n} \) . The phases corresponding to the response of the surface elements adjusted in a way so that \( ({\mathbf {H}}_{d,g}^{\scriptscriptstyle \mathsf {H}}+{\mathbf {H}}_{2,g}^{\scriptscriptstyle \mathsf {H}}{\Phi }{\mathbf {H}}_1) \ge K \) , which is the necessary condition for supporting multi-stream transmission to the K users of a group. This approach of rank improvement through an intelligent surface has been proposed and validated in [2]} for a scenarios with a 2-antenna BS and a 2-antenna UE. In our case, we generalize this approach to a system with an arbitrary number of UEs.
